Difference between revisions of "2021 Fall AMC 12B Problems/Problem 3"
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| − | {{AMC12 box|year=2021 Fall|ab=B|num- | + | {{AMC12 box|year=2021 Fall|ab=B|num-a=4|num-b=2}} |
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 02:18, 4 January 2022
- The following problem is from both the 2021 Fall AMC 10B #4 and 2021 Fall AMC 12B #3, so both problems redirect to this page.
Contents
Problem
At noon on a certain day, Minneapolis is 
degrees warmer than St. Louis. At 
the temperature in Minneapolis has fallen by 
degrees while the temperature in St. Louis has risen by 
degrees, at which time the temperatures in the two cities differ by 
degrees. What is the product of all possible values of 
Solution 1
Let the temperature of Minneapolis be 
, and that of St. Louis be 
. We have 
.
At , either
or
Plug in to solve the two equations respectively to get 
or 
. Hence the answer is 
~Wilhelm Z ~KingRavi ~MRENTHUSIASM
Solution 2
Hence, 
or 6.
Therefore, the answer is 
.
~Steven Chen (www.professorchenedu.com)
See Also
| 2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 2 |
Followed by Problem 4 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
